Implied volatility = calculated or estimated volatility of given finanacial instrument based on current option price.

sticky moneyness = sticky delta.

Volatility - Sticky strike vs Sticky delta


Understanding the sticky delta and sticky strike rules for volatility will help us determine how the volatility skew changes when the markets move.

The sticky strike rule:

Some market players believe that when the stock/index moves, the volatility skew for an option remains unchanged with strike. This behaviour is referred to as the the sticky strike rule. The rule is appliacable when the markets are expected to range bound in near future without significant change in realized volatility.

The sticky delta rule:

There are some market players that tend to believe that the volatility skew remains unchanged with moneyness. For example lets say that the implied volatility for an ATM option is 30% with the index leve being at 100. Now if the index declines to 90, this rule would predict that the implied volatility for 90 stike option would now be 30%. Hence the behaviour is known as sticky moneyness or sticky delta.

The sticky delta rule is more applicable when the markets are trending without a significant change in realized volatility.

The Figure 1 below shows figuratively how the volatility skew gets affected under the two rules. If the current level of the underlier was S0 and the volatility skew for a specific tenor was indicated by L0. Under the sticky strike rule, the skew remains the same L0. Under the sticky delta rule the skew moves in the direction of the underlier move. Thus when the underlier moves from S0 to S1, the new skew is indicated by L1.

figure 1:Volatility skew as the market moves

\Both the sticky strike and sticky delta rules have been proven to provide arbitrage oppportunities. However, these rules do help us understand the risks of the traded products.

It is known that when the market falls, the impied volatility is observed to increase. E. Derman describes a sticky implied tree rule which is consistent with this observation and is also argued to be arbitrage free.

谢谢，您的意思是说这两者之间是并列的关系？只是两种不同的观点吗？还是说在每次变化中,都有这两种因素？
另外在理解上，sticky strike是不是说strike不变，则volatility不变呢？但是strike不是由option合约定死的吗，怎么会变化呢？如果不变化，那sticky strike言下之意就是基础资产价格变化不会引起volatility Skewness的变化，那这样的话，sticky strike还有什么意义呢？不知道我理解得正确吗？请指教了！

vol 可能随着 moneyness 或者strike price而变动；  认为strike 为sticky的时候，哪怕spot price变动，这条vol-strike线不会shift。 如2楼所说，还是原来的函数线L0。 好像是根据那个lognormal的假定推出。
而认为sticky moneyness时，vol curve会从L0 平移到L1。稍微放松了限制。

这里有个比较好的讨论：
https://bbs.pinggu.org/thread-744350-1-1.html